If an equation of the linear function is y = mx + b, then what is m?
Straight lines are very important concepts in mathematics which are represented by linear equations in a cartesian plane. They have a constant slope.
Answer: If an equation of the linear function is y = mx + b, then m is the slope of the line.
Let's understand the solution in detail.
The equation y = mx + b is a linear equation; hence it represents a straight line. Any point (x1, y1) on this line must satisfy this equation as
⇒ y1 = mx1 + b ---------- (1)
Now let's take a random point P(x2, y2) on the given line. Now we have:
⇒ y2 = mx2 + b ---------- (2)
Now if we find equation (2) - (1), we get y2 - y1 = m (x2 - x1)
Hence, m = (y2 - y1) / (x2 - x1)
This formula denotes the change in the vertical coordinates divided by the change in the horizontal coordinates which is the definition for slope.
Hence, if an equation of the linear function is y = mx + b, then m is the slope of the line.